Related papers: On the supersymmetric partition function in QCD-in…
Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the…
We study the open version of the su$(m|n)$ supersymmetric Haldane-Shastry spin chain associated to the $BC_N$ extended root system. We first evaluate the model's partition function by modding out the dynamical degrees of freedom of the…
A recently proposed variational mass expansion approach to dynamical chiral symmetry breakdown is reviewed. We briefly explain how a specific integral ansatz over the analytically continued, arbitrary Lagrangian mass parameter, resums the…
Let the formal power series f in d variables with coefficients in an arbitrary field be a symmetric function decomposed as a series of Schur functions, and let f be a rational function whose denominator is a product of binomials of the form…
We prove a conjecture of Fyodorov and Keating on the supercritical moments of the partition function of the C$\beta$E field or equivalently the supercritical moments of moments of the characteristic polynomial of the C$\beta$E ensemble for…
Using a recent result of L\'arusson and Poletsky regarding plurisubharmonic subextensions we prove a disc formula for the quasiplurisubharmonic global extremal function for domains in complex projective space. As a corollary we get a…
I describe recent progress towards a theory of the NN force which captures the consequences of QCD's chiral symmetry and the pattern of its breaking, and is formulated as an expansion in a ratio of low and high mass scales, M_{lo}/M_{hi}.…
We study chiral-odd quark-antiquark correlation functions suitable for lattice calculations of twist-three nucleon parton distribution functions $h_L(x)$ and $e(x)$, and also the twist-two transversity distribution $\delta q(x)$. The…
Hypergeometric functions of complex matrices were introduced by James in multivariate statistics. These special functions play many roles in random matrix theory. The main goal of this paper is to suggest a new use for them as holomorphic…
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are…
We present models of axion based on supersymmetric chiral gauge theories. In these models, the PQ symmetry is spontaneously broken by the non-perturbative dynamics of chiral gauge theory. Thanks to supersymmetry, IR dynamics of the models…
In [arXiv:1504.07804], Keating, Rodgers, Roditty-Gershon and Rudnick established relationships of the mean-square of sums of the divisor function $d_k(f)$ over short intervals and over arithmetic progressions for the function field $\mathbb…
We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-known Hilbert space case (where it coincides with the…
Our results can be viewed as applications of algebraic combinatorics in random matrix theory. These applications are motivated by the predictive power of random matrix theory for the statistical behavior of the celebrated Riemann…
Egge, Loehr, and Warrington proved a formula for the Schur function expansion of a symmetric function in terms of its expansion in fundamental quasi-symmetric functions. Their formula involves the coefficients of a modified inverse Kostka…
Large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and…
Sylvester showed that the partition function can be written as a sum of the polynomial term and quasiperiodic components called the Sylvester waves. Recently an explicit expression of the Sylvester wave as a finite sum over the Bernoulli…
We introduce a new combinatorial object, semistandard increasing decomposition tableau and study its relation to a semistandard decomposition tableau introduced by Kra\'skiewicz and developed by Lam and Serrano. We also introduce…
Parton distributions are constructed in a statistical physical picture of the nucleon. The chiral properties of QCD lead to strong relations between quarks and antiquarks distributions and the importance of the Pauli exclusion principle is…